The Price of Quota-based Diversity in Assignment Problems
Nawal Benabbou, Mithun Chakraborty, Vinh Ho Xuan, Jakub Sliwinski,, Yair Zick

TL;DR
This paper studies the computational complexity and welfare trade-offs of assignment problems with diversity constraints, motivated by Singapore's public housing policy, and proposes approximation algorithms and bounds for the welfare loss.
Contribution
It introduces the assignment with type constraints problem, analyzes its intractability, and provides approximation algorithms and welfare loss bounds.
Findings
Adding diversity constraints makes the problem NP-hard.
A 1/2-approximation algorithm is proposed.
Simulations illustrate the practical impact of constraints.
Abstract
We introduce and analyze an extension to the matching problem on a weighted bipartite graph: Assignment with Type Constraints. The two parts of the graph are partitioned into subsets called types and blocks; we seek a matching with the largest sum of weights under the constraint that there is a pre-specified cap on the number of vertices matched in every type-block pair. Our primary motivation stems from the public housing program of Singapore, accounting for over 70% of its residential real estate. To promote ethnic diversity within its housing projects, Singapore imposes ethnicity quotas: each new housing development comprises blocks of flats and each ethnicity-based group in the population must not own more than a certain percentage of flats in a block. Other domains using similar hard capacity constraints include matching prospective students to schools or medical residents to…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
